December 7, 2009

Student 1: Yes, I'm married and have three wounderful children.Student 2: That's great! How old are they?Student 1: Well, the product of their ages is 36.Student 2: Hmm. That doesn't tell me enough. Give me another clue.Student 1: OK. the sum of their ages is the number on that building across the street.Student 2: (After a few minutes of thinking with the aid of pencil and paper) Ah ha! I've almost got it but I still need another clue.Student 1: Very well. The oldest one has red hair.Student 2: I've got it!

8 comments:

13 is the only sum of two sets of three numbers whose product is 36. Therefore, 13 is the number of the building across the street. His children were either 6,6,1 or 9,2,2. When he stated that the oldest one has red hair, the option of 6,6,1 became invalid

You could argue that since one twin was born shortly before the other that they were therefore the oldest, but Student 2 clearly doesn't think so since they worked out their ages. So 2,2,9 is certainly correct.

Hey, Tiger! - if your wife won't let you have all of those girls any more, how about sending one or two my way :-)

The thing "wrong" with 2,3,6 is that there is only that one answer summing up to 11. Then the ages would have been clear after the house number. 13 is the only sum with two answers (2,2,9 and 1,6,6) and thus requires the tie-breaker...

However, the second clue, which was that the sum of their ages was the number of the building across the street, was not sufficient. If the number had been 11, there is only one set of numbers whose sum is 11 and product is 36, so that can't be it, since student 2 still needed more information.

The information s/he needed was whether the two oldest children were twins or the two youngest ones - 6,6,1 or 9,2,2. When Student 1 said "The oldest one...", that's what made it clear.